【作者】 马婷；

【导师】 梁学章；

【作者基本信息】 吉林大学 ， 计算数学， 2007， 硕士

【摘要】 反向工程是一门正在迅速发展中的学科分支,目前还处于不断研究和探讨之中。而反向工程中一个重要的问题,就是点云数据图像的重建问题。该问题包括点云数据的获取,预处理和最后曲面的显示等步骤。本文重点讨论预处理中的点云数据的配准问题和点云曲面的显示问题。我们给出了点云曲面显示的一种简捷方法,对此方法进行了理论分析,并将其与最小二乘方法进行了数值实验比较。同时,我们针对兔子点云的配准问题,利用朱延娟等人提出的配准算法,进行了编程数值实验,得到了较好的配准效果,并分析了影响精度的因素。更多还原

【Abstract】 Computer Aided Design （CAD）, coming up with the development of computer and the modern industry, today it is still regarding geometric modeling of industry product as its research object. There are two methods in CAD. One is a design member design an object according to the certain method under the condition of object is nonexistent, it is normal direction, and its workload is very huge. Another one is basis the object which has already existed, using the data acquisition which was obtained on the object’s surface, we can receive the point cloud data in an order or disorder, then surface or curve will be reconstructed through handling of the point cloud data. Thus CAD that computer can identify will be get. It is reverse engineering in the development. Reverse engineering is an important technology in realizing the duplication and modifying of freeform surface parts, which includes measuring, modeling, manufacturing and inspecting of freeform surface. Reverse engineering is a basic problem in geometric modeling, has great common sense and practicality, and it is complement with CAD/CAM/CAE. This article is based on the main problem that we should solve in reverse engineering, our primary research is on the pre-handling of the point cloud data, and surface reconstruction.Pre-handling of the point cloud data is an important step, which completes the digital of object model. Because the obtained point cloud data is more than one piece, we could register the point cloud data, using the geometric nature of point cloud data. Through the methods of rotation and translation, we can register the point cloud data which is obtained from several times and a variety of measuring, from the own local coordinates to overall coordinates.Let p i and its k-nearest points be N（ p i）, which can be approximated by the quadric parameters surface. Set the quadric parameters equation as: We can use the principle of least squares, derive the coefficient matrixQ , and get the equation of quadric parameters surface r （u ,v）. The unit normal vector of the surface is Calculate the first and the second basic quantity of the \ the average curvature and then according to the above values, we canget the main curvature k₁,k₂ Here, we finished the computation of the normal vector and curvature of every data point.Given the two point sets of cloud data which waiting for registration S₁ = {p₁¹,p₂¹,,p_m¹}and S₂ = { p₁²,p₂²,,p_n²}, if k₁,k₂ of p i are zero, discarding p i. It is said that p i will not be entered to the set of the matching points. Applying the maximum and the minimum curvature, filtering to the matching points, selecting following the principle All the matching points, which are approximate enough, constitute a table. For every matching point （ p_i¹ , p_j²） on the table, the rigid transformations that map p_i¹ to p_j² are computed, making the direction of normal vectors n_i¹ and n_j²coincide.Compute the rotate transformations of every matching point （n i¹ , n_j²）, then compute translation vectors, so that matching points p_i¹ and p_j² overlap. Therefore, we can get the rigid transformations that make p_i¹ and p_j² overlapped.A hash table is constituted from the coordinate transformations in 3D space. The target transformation that makes the most count in this table is employed to register the two point cloud data. If we want to get more precision result, we can use the result of the rough registration, and then the iterative closet point algorithm leads to perfect registration.For the display of point cloud data, we propose the facility display usage. Take a piece of point cloud data, divide it into several small pieces and process B-spline surface display. Let point cloud data （data point） be control point of B-spline surface and approximate the surface, also, we give the theory proof of this method. In addition, we could approximate with piecewise least square for data, after obtaining the display of every small piece, we put together the adjacent small pieces and obtain the continuous smooth figure with G 0. Following, we compare the two display methods in the front and illuminate the effectiveness of the algorithm in this paper. At the end of the article, we show the numerical experiment of the point cloud data of the rabbits, and implement the algorithm.更多还原